practice questions for Test 1 solution

practice questions for Test 1 solution - AMS310 PRETEST 1...

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AMS310 PRETEST 1 practice questions for Test 1 I. SHORT ANSWER/MULTIPLE CHOICE QUESTIONS. 1. ALL QUIZ QUESTIONS Given f(x)= 0.1x for x=1,2,3, 4. 2 (a) What is the value of μ x ? (b) What is the value of σ x ? 3. Given X has Poisson probability distribution with λ =3.2, (a)what is the value of μ ? (b) What is the value of σ 2 ? 4. Evaluate = - - 10 0 2 )! 10 ( ! ! 10 ) 3 ( x x x x 0.3 x 0.7 10-x . 5. P(A)= 0.4, P(A|B)=0.4, so P(A| B ) =___. Ans. 0.4. 6. X has Poisson probability distribution with λ = 5. Use Table 2 to find P(X 4). 7. For a particular course, there are three grades, 0,1,2, 3 and 4, with 4=A etc. The cumulative distribution of the course grades is as follows: F(4)=1.0, F(3)=0.85, F(2)=0.65, F(1)=0.2 and F(0)=0.1. (a) What is the probability a student will receive a B? i.e., P(X=3)? (b) What is the probability that he will receive a score of C or less, i.e., P(X 2)? Ans.(a) 0.20 (b) 0.65 8. Suppose X takes on values from 0 to 10 with f(0)=0.01 and f(10)= 0.05, then the standard deviation (a)must be less than 10 (b)can equal 10 (c) can equal 0 (d) can be more than 10. 9. If A and B are independent, then which of the following is false? (a) P(A|B)=P(A) (b)P(A B) < P(A) + P(B) (c) P(A B)=P(A)xP(B) (d) A, B mutually exclusive. Ans. (D) 10. Suppose we toss a fair die ie., S={1,2,3,4,5,6} Let {A}={1,2,4} and let B={1,2, 5} and let C={3,5,6} The events {A} and {C} are (a)mutually exclusive and dependent (b)mutually exclusive and independent (c)Not mutually exclusive and independent (d) not mutually exclusive and dependent. Answer. (a) II. Longer problems: 1. Let F={ a randomly sampled person works on the 1st Floor} and A = {a randomly sampled person has an accident}. Suppose we are told that 2% of those who work on the first floor have accidents and that 1% of those who don’t work on the first floor have accidents. Suppose we are also told that 75% work on the first floor and 25% do not. (a)Pr(A|F)= ___. (b)Pr(A F)= __ (c)Pr(A F’)=__ (d)Pr (A) =____ (e)Pr(F|A)= __ (f) Is having an accident independent of what floor you work? Write a sentence indicating where you would like to work and the percentages which prove your point. Ans. (a) 0.02 (b) 0.015 . (c)0.0025 . (d) 0.0175 (e) 0.8571 (f) A, F are not independent. I would not want to work on the first floor. On the first floor the percentage of individuals having accidents is 2% as compared for 1% of workers on all other floors.
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